(Auteur) The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

(Auteur) For multitemporal analysis of synthetic aperture radar (SAR) images acquired with a terrain observation by progressive scan (TOPS) mode, all acquisitions from a given satellite track must be coregistered to a reference coordinate system with accuracies better than 0.001 of a pixel (assuming full SAR resolution) in the azimuth direction. Such a high accuracy can be achieved through geometric coregistration, using precise satellite orbits and a digital elevation model, followed by a refinement step using a time-series analysis of coregistration errors. These errors represent the misregistration between all TOPS acquisitions relative to the reference coordinate system. We develop a workflow to estimate the time series of azimuth misregistration using a network-based enhanced spectral diversity (NESD) approach, in order to reduce the impact of temporal decorrelation on coregistration. Example time series of misregistration inferred for five tracks of Sentinel-1 TOPS acquisitions indicates a maximum relative azimuth misregistration of less than 0.01 of the full azimuth resolution between the TOPS acquisitions in the studied areas. Standard deviation of the estimated misregistration time series for different stacks varies from 1.1e-3 to 2e-3 of the azimuth resolution, equivalent to 1.6-2.8 cm orbital uncertainty in the azimuth direction. These values fall within the 1-sigma orbital uncertainty of the Sentinel-1 orbits and imply that orbital uncertainty is most likely the main source of the constant azimuth misregistration between different TOPS acquisitions. We propagate the uncertainty of individual misregistration estimated with ESD to the misregistration time series estimated with NESD and investigate the different challenges for operationalizing NESD.

(Auteur) Terrestrial reference frames (TRF), such as the ITRF2008, are primary products of geodesy. In this paper, we present TRF solutions based on Kalman filtering of very long baseline interferometry (VLBI) data, for which we estimate steady station coordinates over more than 30 years that are updated for every single VLBI session. By applying different levels of process noise, non-linear signals, such as seasonal and seismic effects, are taken into account. The corresponding stochastic model is derived site-dependent from geophysical loading deformation time series and is adapted during periods of post-seismic deformations. Our results demonstrate that the choice of stochastic process has a much smaller impact on the coordinate time series and velocities than the overall noise level. If process noise is applied, tests with and without additionally estimating seasonal signals indicate no difference between the resulting coordinate time series for periods when observational data are available. In a comparison with epoch reference frames, the Kalman filter solutions provide better short-term stability. Furthermore, we find out that the Kalman filter solutions are of similar quality when compared to a consistent least-squares solution, however, with the enhanced attribute of being easier to update as, for instance, in a post-earthquake period.

(Auteur) The usefulness of relativistic space-times for the description of the Earth’s gravitational field is investigated. A variety of exact vacuum solutions of Einstein’s field equations (Schwarzschild, Erez and Rosen, Gutsunayev and Manko, Hernández-Pastora and Martín, Kerr, Quevedo, and Mashhoon) are investigated in that respect. It is argued that because of their multipole structure and influences from external bodies, all these exact solutions are not really useful for the central problem. Then, approximate space-times resulting from an MPM or post-Newtonian approximation are considered. Only in the DSX formalism that is of the first post-Newtonian order, all aspects of the problem can be tackled: a relativistic description (a) of the Earth’s gravity field in a well-defined geocentric reference system (GCRS), (b) of the motion of solar system bodies in a barycentric reference system (BCRS), and (c) of inertial and tidal terms in the geocentric metric describing the external gravitational field. A relativistic SLR theory is also discussed with respect to our central problem. Orders of magnitude of many effects related to the Earth’s gravitational field and SLR are given. It is argued that a formalism with accuracies better than of the first post-Newtonian order is not yet available.

(Auteur) This paper addresses the problem of debris estimation which is one of the most important initial challenges in the wake of a disaster like the Great East Japan Earthquake and Tsunami. Reasonable estimates of the debris have to be made available to decision makers as quickly as possible. Current approaches to obtain this information are far from being optimal as they usually rely on manual interpretation of optical imagery. We have developed a novel approach for the estimation of tsunami debris pile heights and volumes for improved emergency response. The method is based on a stereo-synthetic aperture radar (stereo-SAR) approach for very high-resolution polarimetric SAR. An advanced gradient-based optical-flow estimation technique is applied for optimal image coregistration of the low-coherence non-interferometric data resulting from the illumination from opposite directions and in different polarizations. By applying model based decomposition of the coherency matrix, only the odd bounce scattering contributions are used to optimize echo time computation. The method exclusively considers the relative height differences from the top of the piles to their base to achieve a very fine resolution in height estimation. To define the base, a reference point on non-debris-covered ground surface is located adjacent to the debris pile targets by exploiting the polarimetric scattering information. The proposed technique is validated using in situ data of real tsunami debris taken on a temporary debris management site in the tsunami affected area near Sendai city, Japan. The estimated height error is smaller than 0.6 m RMSE. The good quality of derived pile heights allows for a voxel-based estimation of debris volumes with a RMSE of 1099 m3. Advantages of the proposed method are fast computation time, and robust height and volume estimation of debris piles without the need for pre-event data or auxiliary information like DEM, topographic maps or GCPs.